diff --git a/checks/Check.hs b/checks/Check.hs
index f85e881..055b946 100644
--- a/checks/Check.hs
+++ b/checks/Check.hs
@@ -159,7 +159,7 @@ checkInitVar m graph startNode
        -- Now we check that for every variable read in each node, it has already been written to by then
        mapM_ (checkInitVar' vwb) (map readNode labelledConnectedNodes)
   where
-    connectedNodes = dfs [startNode] graph
+    connectedNodes = udfs [startNode] graph
 
     -- Gets all variables read-from in a particular node, and the node identifier
     readNode :: (Node, FNode m UsageLabel) -> (Node, ExSet Var)
diff --git a/checks/UsageCheckAlgorithms.hs b/checks/UsageCheckAlgorithms.hs
index 2c3b402..5f22a44 100644
--- a/checks/UsageCheckAlgorithms.hs
+++ b/checks/UsageCheckAlgorithms.hs
@@ -132,7 +132,7 @@ checkPar getRep f g = mapM f =<< allParItems
 findReachDef :: forall m. Monad m => FlowGraph m UsageLabel -> Node -> Either String (Map.Map Node (Map.Map Var (Set.Set (Maybe
   A.Expression))))
 findReachDef graph startNode
-  = do r <- flowAlgorithm graphFuncs (nodes graph) (startNode, Map.empty)
+  = do r <- flowAlgorithm graphFuncs (udfs [startNode] graph) (startNode, Map.empty)
        -- These lines remove the maps where the variable is not read in that particular node:
        let r' = Map.mapWithKey (\n -> Map.filterWithKey (readInNode' n)) r
        return $ Map.filter (not . Map.null) r'
diff --git a/flow/FlowAlgorithms.hs b/flow/FlowAlgorithms.hs
index 296c5d4..c9e25fd 100644
--- a/flow/FlowAlgorithms.hs
+++ b/flow/FlowAlgorithms.hs
@@ -53,6 +53,11 @@ data GraphFuncs n e result = GF {
 -- (i.e. where nodesToProcess returns the empty list) in the list except the
 -- starting node.
 --
+-- The implication of the above is that you should /not/ pass as the second
+-- parameter all the nodes in the graph (unless you /know/ that it is fully
+-- connected).  Instead you should pass the connected nodes, using @(udfs [startNode]
+-- graph)@.
+--
 -- The general idea of iterative data-flow is that all nodes start out with
 -- a default "guessed" value.  Then each node is processed in turn by using
 -- the previous value (to start with, the default value), and the values of